ISBN-10: 1420077619

ISBN-13: 9781420077612

Edition: 5th 2010 (Revised)

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Description:

The fifth edition of this classic text retains its original flavor, while providing a large collection of time tested commonly used nonparametric techniques, including both hypothesis tests and confidence intervals. It presents in-depth coverage of the theory and methods of the most widely used nonparametric procedures in statistical analysis and offers example applications appropriate for the social, behavioral, and life sciences. This new edition is thoroughly revised, rewritten, and reorganized as needed, with updated and revised examples and all essential user-friendly tables for easy implementation. No other nonparametric book does it this well at this level, or in a more accessible manner.

Lokenath Debnath is Professor of the Department of Mathematics and Professor of Mechanical and Aerospace Engineering at the University of Central Florida in Orlando. He received his M.Sc. and Ph.D. degrees in pure mathematics from the University of Calcutta, and obtained D.I.C. and Ph.D. degrees in applied mathematics from the Imperial College of Science and Technology, University of London. He was a Senior Research Fellow at the University of Cambridge and has had visiting appointments to several universities in the United States and abroad. His many honors and awards include two Senior Fulbright Fellowships and an NSF Scientist award to visit India for lectures and research. Dr. Debnath is author or co-author of several books and research papers in pure and applied mathematics, and serves on several editorial boards for scientific journals. He is the current and founding Managing Editor of the International Journal of Mathematics and Mathematical Sciences.

Preface to the Fifth Edition

Introduction and Fundamentals

Introduction

Fundamental Statistical Concepts

Basic Definitions

Moments of Linear Combinations of Random Variables

Probability Functions

Distributions of Functions of Random Variables Using the Method of Jacobians

Chebyshev's Inequality

Central Limit Theorem

Point and Interval Estimation

Hypothesis Testing

P Value

Consistency

Pitman Efficiency

Randomized Tests

Continuity Correction

Order Statistics, Quantiles, and Coverages

Introduction

Quantile Function

Empirical Distribution Function

Empirical Quantile Function

Statistical Properties of Order Statistics

Cumulative Distribution Function of X<sub>(r)</sub>

Probability Density Function of X<sub>(r)</sub>

Probability-Integral Transformation

Joint Distribution of Order Statistics

Distributions of the Median and Range

Distribution of the Median

Distribution of the Range

Exact Moments of Order Statistics

kth Moment about the Origin

Covariance between X<sub>(r)</sub> and X<sub>(s)</sub>

Large-Sample Approximations to the Moments of Order Statistics

Asymptotic Distribution of Order Statistics

Tolerance Limits for Distributions and Coverages

One-Sample Coverages

Two-Sample Coverages

Ranks, Block Frequencies, and Placements

Summary

Problems

Tests of Randomness

Introduction

Tests Based on the Total Number of Runs

Exact Null Distribution of R

Moments of the Null Distribution of R

Asymptotic Null Distribution

Discussion

Applications

Tests Based on the Length of the Longest Run

Rims Up and Down

Applications

A Test Based on Ranks

Summary

Problems

Tests of Goodness of Fit

Introduction

The Chi-Square Goodness-of-Fit Test

The Kolmogorov-Smirnov (K-S) One-Sample Statistic

Applications of the Kolmogorov-Smirnov (K-S) One-Sample Statistics

One-Sided Tests

Confidence Bands

Determination of Sample Size

Lilliefors's Test for Normality

Lilliefors's Test for the Exponential Distribution

Anderson-Darling (A-D) Test

Visual Analysis of Goodness of Fit

Summary

Problems

One-Sample and Paired-Sample Procedures

Introduction

Confidence Interval for a Population Quantile

Hypothesis Testing for a Population Quantile

The Sign Test and Confidence Interval for the Median

P value

Normal Approximations

Zero Differences

Power Function

Simulated Power

Sample Size Determination

Confidence Interval for the Median

Problem of Zeros

Paired-Sample Procedures

Applications

Rank-Order Statistics

Treatment of Ties in Rank Tests

Randomization

Midranks

Average Statistic

Average Probability

Least Favorable Statistic

Range of Probability

Omission of Tied Observations

The Wilcoxon Signed-Rank Test and Confidence Interval

The Problem of Zero and Tied Differences

Power Function

Simulated Power

Sample Size Determination

Confidence-Interval Procedures

Paired-Sample Procedures

Use of Wilcoxon Statistics to Test for Symmetry

Applications

Summary

Problems

The General Two-Sample Problem

Introduction

The Wald-Wolfowitz Runs Test

The Problem of Ties

Discussion

The Kolmogorov-Smirnov (K-S) Two-Sample Test

One-Sided Alternatives

Ties

Discussion

Applications

The Median Test

Applications

Confidence-Interval Procedure

Power of the Median Test

The Control Median Test

Curtailed Sampling

Power of the Control Median Test

Discussion

Applications

The Mann-Whitney U Test and Confidence Interval

The Problem of Ties

Confidence-Interval Procedure

Sample Size Determination

Discussion

Summary

Problems

Linear Rank Statistics and the General Two-Sample Problem

Introduction

Definition of Linear Rank Statistics

Distribution Properties of Linear Rank Statistics

Usefulness in Inference

Problems

Linear Rank Tests for the Location Problem

Introduction

The Wilcoxon Rank-Sum Test and Confidence Interval

Applications

Other Location Tests

Terry-Hoeffding (Normal Scores) Test

van der Waerden Test

Percentile Modified Rank Tests

Summary

Problems

Linear Rank Tests for the Scale Problem

Introduction

The Mood Test

The Freund-Ansari-Bradley-David-Barton Tests

The Siegel-Tukey Test

The Klotz Normal-Scores Test

The Percentile Modified Rank Tests for Scale

The Sukhatme Test

Confidence Interval Procedures

Other Tests for the Scale Problem

Applications

Summary

Problems

Tests of the Equality of k Independent Samples

Introduction

Extension of the Median Test

Extension of the Control Median Test

The Kruskal-Wallis One-Way ANOVA Test and Multiple Comparisons

Applications

Other Rank-Test Statistics

Tests against Ordered Alternatives

Applications

Comparisons with a Control

Case I: ï¿½<sub>1</sub> Known

Case II: ï¿½<sub>1</sub> Unknown

Applications

Summary

Problems

Measures of Association for Bivariate Samples

Introduction: Definition of Measures of Association in a Bivariate Population

Kendall's Tau Coefficient

Null Distribution of T

The Large-Sample Nonnull Distribution of Kendall's Statistic

Tied Observations

A Related Measure of Association for Discrete Populations

Use of Kendall's Statistic to Test against Trend

Spearman's Coefficient of Rank Correlation

Exact Null Distribution of R

Asymptotic Null Distribution of R

Testing the Null Hypothesis

Tied Observations

Use of Spearman's R to Test against Trend

The Relations between R and T; E(R), T, and ï¿½

Another Measure of Association

Applications

Summary

Problems

Measures of Association in Multiple Classifications

Introduction

Friedman's Two-Way Analysis of Variance by Ranks in a k x n Table and Multiple Comparisons

*A minimum purchase of $35 is required. Shipping is provided via FedEx SmartPost®
and FedEx Express Saver®. Average delivery time is 1 – 5 business days, but
is not guaranteed in that timeframe. Also allow 1 - 2 days for processing. Free shipping is eligible only in the continental United States and excludes
Hawaii, Alaska and Puerto Rico. FedEx service marks used by permission."Marketplace"
orders are not eligible for free or discounted shipping.